The non-destructive investigation of samples is an important task in various technical fields like material sciences, medical examinations, archaeology, construction technique, techniques concerning security matters etc. One approach for obtaining an image of a sample e.g. by computer tomography (CT) is based on an irradiation trough an object plane from different projection directions with X-rays, followed by a reconstruction of the object plane on the basis of attenuation data measured at different directions. The entirety of the measured attenuation data can be described in terms of so-called Radon data in a Radon space.
The most relevant conventional reconstruction methods known today can be summarized as methods based on the iterative reconstruction or those based on the so-called filtered back-projection. The iterative reconstruction methods have essential disadvantages in terms of extremely long calculation times. On the other hand, the filtered back-projection method, which relies on the so-called Fourier-slice theorem, has a general disadvantage due to an interpolation step in the reconstruction, which results in errors and artifacts that have a tendency to increase with increasing space frequency. Another problem of the filtered back-projection method is related to the discretization of the Radon data from which the image data have to be reconstructed. To get an optimal filtered back-projection reconstruction it would be necessary to exactly match the projected irradiation rays with detector elements of a detector. This is in general not the case. For this reason, uncertainties or smoothing effects from the reconstruction of Radon data by means of filtered back-projection algorithms are introduced.
T. Bortfeld et al. have described an algorithm for the reconstruction of two-dimensional images from a plurality of projections along the projection directions (“Phys. Med. Biol.”, Vol. 44, 1999, p. 1105-1120). With this algorithm, the projections are represented as decompositions, which are subjected to the above filtered back-projection reconstruction. The projections are measured e.g. with a fan beam geometry, wherein attenuation values according to distinct projection lines with even angular intervals relative to each other are measured. The single projection lines measured with different projection directions of the fan beam can be resorted for providing parallel projections to be used for the image reconstruction. The algorithm of T. Bortfeld et al. has not yielded a practical implementation. The algorithm assumes an ideal fan beam geometry, which is not available in practice. Therefore, the T. Bortfeld et al. algorithm requires an interpolation step like the conventional filtered back-projection. Furthermore, the T. Bortfeld et al. algorithm has an essential disadvantage in terms of artifacts occurring in the reconstructed images.
The disadvantages of the filtered back-projection procedures and the method of T. Bortfeld et al. can be avoided with an image reconstruction method, which is described in the non-published European patent application EP 04031043.5. With this method, the image function is determined from Radon data comprising a plurality of projection functions measured corresponding to the plurality of predetermined projection directions. The image function is determined as a sum of polynomials multiplied with values of the projection functions. In practical implementations, this image reconstruction is based on the measurement of attenuation values corresponding to discrete irradiation beam components having equal angles relative to each other. According to non-published EP 04031043.5, the discrete beam components can be generated with a fan beam geometry by using a radiation source 210′ equipped with a source mask 211′ as schematically illustrated in FIG. 12. The source mask 211′ comprises a shielding plate 212′ for example made by tungsten with through holes 213′. The shielding plate 212′ of the source mask 211′ can have a planar shape as shown in FIG. 12 or a cylindrical shape. The through holes 213′ are arranged such that projection lines starting at the radiation source cross a circle with detector elements with an equal arc length spacing.
In contrast to the T. Bortfeld et al. algorithm, the image reconstruction of unpublished EP 04031043.5 can be used to replace the conventional filtered back-projection algorithm. Therefore, the artifacts introduced by the interpolation in filtered back-projection could be avoided. Nevertheless, it has been found that the image reconstruction according to EP 04031043.5 in practice may have disadvantages in terms of artifacts in the reconstructed image (so-called aliasing artifacts).
Current developments in computed tomography have provided so-called multi-slice-CT and CT-systems based on flat panel technology. These developments are suffering from three further major problems. First of all, the amount of data is very large, the reconstruction time for such an amount of data is too long or the computers needed to handle such data are too expensive. The second problem results from the planar geometry of the detector, which generally is not adapted to the circle geometry of conventional CT devices. Finally, resolution of low contrast details is restricted due to scattered radiation.
The above disadvantages are associated not only with the conventional CT imaging, but also with all available reconstruction methods related to Radon data.